An armed man, dressed in the uniform of the Ukrainian riot police, speaks with a woman near the regional administration building in Luhansk, eastern Ukraine.

Pro-Russian separatists in eastern Ukraine are taking cover in civilians' apartments during government-backed air strikes, officials and residents said, as Moscow lashed out at the Ukrainian military for committing "crimes" against its people in the east.

The Ukrainian military was unable to use its air forces against separatists who attacked a border patrol near Luhansk on Monday because militants rushed into residential buildings for cover, said Vladislav Seleznyov, a spokesman for the government's so-called anti-terror operation, RBK-Ukraine reported.

"Terrorists who have tried to capture a border patrol on the outskirts of the city are not only seizing residents' apartments to use as their firing points, but also prevent people from leaving, essentially taking them hostage," Bryhunets said Monday on his Facebook page, as the fighting raged in Luhansk.

Local resident Olha Tatarenko, a teacher, gave a similar account on her blog on Russia's Ekho Moskvy website, but said rebels allowed civilians to leave — giving them 15 minutes to gather their identity documents.

"Now I know why people stupidly say the national guard are firing on the homes of peaceful citizens … because [separatist] snipers are ensconced in these 'civilian homes' and are shooting at Ukrainian soldiers!" she wrote.

Following Monday's battle in eastern Ukraine, the Russian Foreign Ministry accused Ukraine's authorities of committing "yet another crime against its own people," accusing the military in a statement of launching an air strike on the Luhansk regional administration building and killing civilians.

A spokesman for government forces, Oleksiy Dmytrashevsky said no such air strike had taken place, and that an explosion in the building appeared to have been caused by the militants' "careless or unskilled handling of firearms and explosives," the Ukrainian-language website of Radio Free Europe/Radio Liberty reported.

Tatarenko, the teacher from Luhansk, also cast doubt on Russia's claims that the administrative building was hit by government forces, referencing photographs of the building that appeared to show no damage to the roof or windows that would be consistent with an airstrike.

"One can only feel proud for our domestic weaponry, which has learned to fire in zig-zags," she said in a sarcastic remark on her Ekho Moskvy blog.

While Western and Ukrainian officials have accused Russia of waging a proxy war in the region, Moscow has sought to put a distance between itself and the fighting.

Photographer Maria Turchenkova said Monday on her Ekho Moskvy blog that separatists in Donetsk had loaded onto a truck the bodies of dead Russian fighters — killed while battling on the rebel side — and tried to give them a solemn farewell before sending the truck across the border.

In an apparent attempt to gain the Kremlin's support and attention, separatists had invited Russian television crews to report the Russians' final trip home, but not a single Russian state-run television channel reported the news, according to Turchenkova.

A few journalists "were the only ones seeing Russians who had died in the battle for Donetsk airport on their way home from Ukraine," Turchenkova said on her blog.